1. Field of the Invention
The present invention generally relates to a statistical method which provides time-to-event estimates for oilfield equipment, and, more particularly a method which utilizes survival analysis techniques for analyzing time-to-event data.
2. Description of the Prior Art
Currently oilfield tool (and equipment) performance prediction and analysis is conducted in an ad hoc fashion with varying degrees of sophistication and quality of interpretation. A major concern is that of bias being introduced into the analysis and hence into the results, either through the exclusion of data or by assumptions about the performance of equipment at the time of data sampling. At the time of an analysis, the analyst has a population of capital intensive oilfield equipment from which to draw data. Some of this equipment may have already failed at the time of the data was extracted, while other installed equipment is still fully operational and had not failed at the time the data was extracted. This latter subset of the population has been the subject of improper analysis in the past in two particulars: (i) complete exclusion of the data set; or (ii) the inaccurate assumption that, at the time the data was drawn, the equipment had failed.
Survival analysis is a statistical methodology and testing hypothesis of time-to-event data that has, for example, been applied in the medical field to analyze time-to-death of a patient after surgery, the cessation of smoking, the reoccurrence of disease. For most statistical applications, models for probability distributions are usually described in terms of:                Probability Density Function (pdf) ƒ(t): a function whose integral over a given range is equal to the probability of taking a value in that range.        Distribution Function F(t) (cumulative density function): the probability of the event occurring by time t.For survival analysis, however, it is appropriate to work with different functions characterizing the distribution:        Survival Function S(t): the probability of surviving at least to time t [sometimes known as a reverse cumulative density function: 1-F(t)].        Hazard Function h(t): the potential of failure in the next instant given survival to time t.        
An Explanatory Variable (EV) is a variable that may influence equipment behavior. In conventional product-limit analysis, the investigation of a single EV requires partitioning of data set into subsets for each level of the EV and analysis is then performed independently on each subset. This has the effect of thinning the data which may result in less reliable statistics. In an investigation of two or more EVs, this problem is compounded. For example, if it is desired to predicate how an Electrical Submersible Pump (ESP) System would behave in a deviated well (true/false) and an openhole well (true/false), four data subsets exist to examine independently. As the number of EVs in an analysis is increased, there will be some subsets that are sparsely populated.